Let $f$ be the function given by $f(x)=2e^{3x}$ and $g$ be the function given by $g(x)=4x^3$. At what value of $x$ do the graphs of $f$ and $g$ have parallel tangent lines?

Summary Submit Skip Question

Take the derivative of both functions:

Setting the derivative of each function equal to each other:

$$6e^{3x}=12x^2$$

In our calculator, we plot the graph of both derivatives. Use the intersect option to find the $x$ value that corresponds to the solution.

$$x \approx \boxed{-0.39}$$